THE MULTIPLICATION ALGORITHM : Some Class 3 children in a nearby school had been taught the standard multiplication. Algorithm, and had even done reasonably well in the tests based on it. A year later, in Class 4, several of them made errors like:
When a child, who had made the first kind of error, was asked how she had got the answer, she patiently told us, "9 x 3 = 27, so 7 is here (in the ones place) and carry-over 2. Then 4 + 2 is 6 and 6 x 3 = 18, so 8 is here (in the tens place) and carry-over 1. Then 6 + 1 is 7 and 7 x 3 = 21, so the answer is 2187."
None of these children realised how absurd their answers were because they had not understood what multiplication is. Clearly, their teacher's strategy didn't work. The method he had adopted was to just feed the children the standard algorithm through a few examples, and make them do several problems based on it, mechanically.
If this strategy doesn't work, then which one would? To evolve one, we must first look into the processes involved in the algorithm, and why it works.
Understanding the algorithm requires an understanding of place value, multiplication as repeated addition, carry-over and the distributive law of multiplication with respect to addition. In Units 6 and 7 we have suggested several activities for helping a child understand 'place value' and 'carry-over'. So, assuming that the child has done these activities, and has also understood multiplication as repeated addition, let us see how we can help her realise the utility of the distributive law.